logninv

Syntax

X = logninv(P,mu,sigma)
[X,XLO,XUP] = logninv(P,mu,sigma,pcov,alpha)

Description

X = logninv(P,mu,sigma) returns
values at P of the inverse lognormal cdf with distribution
parameters mu and sigma. mu and sigma are
the mean and standard deviation, respectively, of the associated normal
distribution. mu and sigma can
be vectors, matrices, or multidimensional arrays that all have the
same size, which is also the size of X.
A scalar input for P, mu, or sigma is
expanded to a constant array with the same dimensions as the other
inputs.

[X,XLO,XUP] = logninv(P,mu,sigma,pcov,alpha) returns
confidence bounds for X when the input parameters mu and sigma are
estimates. pcov is the covariance matrix of the
estimated parameters. alpha specifies 100(1 - alpha)% confidence
bounds. The default value of alpha is 0.05. XLO and XUP are
arrays of the same size as X containing the lower
and upper confidence bounds.

logninv computes confidence bounds for P using
a normal approximation to the distribution of the estimate

μ^+σ^q

where q is the Pth quantile
from a normal distribution with mean 0 and standard deviation 1. The
computed bounds give approximately the desired confidence level when
you estimate mu, sigma, and pcov from
large samples, but in smaller samples other methods of computing the
confidence bounds might be more accurate.

The lognormal inverse function is defined in terms of the lognormal
cdf as